著者

藤川 正毅 石川 清貴 真壁 朝敏 田中 真人 笹川 崇 表 竜二

出版者

一般社団法人 日本機械学会

雑誌

日本機械学会論文集 (ISSN:21879761)

巻号頁・発行日

pp.15-00454, (Released:2016-01-15)

参考文献数

13

被引用文献数

6 5

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This paper proposes a novel implementation scheme of geometrically nonlinear finite element programs, which automatically compute exact internal force vectors and element stiffness matrices by numerically differentiating a strain energy function at each element. This method can significantly simplify the complex implementation procedure which is often observed in conventional finite element implementations, since it never requires B matrices, stress tensors, and elastic tensors by hand. The proposed method is based on a highly accurate numerical derivatives which use hyper-dual numbers and never suffer from any round-off and truncation errors. Several numerical examples are performed to demonstrate the effectiveness and robustness of the proposed method.

著者

藤川 正毅 田中 真人 井元 佑介 三目 直登 浦本 武雄 山中 脩也

出版者

一般社団法人 日本機械学会

雑誌

日本機械学会論文集 (ISSN:21879761)

巻号頁・発行日

vol.86, no.881, pp.19-00256, 2020 (Released:2020-01-25)

参考文献数

20

被引用文献数

1

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A numerical calculation scheme for stress and its consistent tangent moduli with hyper-dual numbers(HDN) for Ogden-type hyperelastic material model was proposed. The main advantage of this scheme is that once the framework is coded, any Ogden-type hyperelastic material model can be implemented by only re-coding the strain energy density function. In this scheme, the new differentiation method for eigenvalue and eigenvector of the symmetric matrices with HDN were proposed. The proposed method can calculate the eigenvalue and eigenvector in non-real part analytically by using the eigenvalue and eigenvector in real part, in case that all eigenvalues in real part are not multiple root. We implemented the Neo-Hookean model and the Ogden model with the proposed scheme, to confirm the effectiveness and robustness of this method, and applied it to some examples. As the results, it was confirmed that the numerical results of the proposed method showed good agreement with analytical ones.

著者

田中 真人 藤川 正毅 儀間 麻衣

出版者

日本学術会議 「機械工学委員会・土木工学・建築学委員会合同IUTAM分科会」

雑誌

理論応用力学講演会 講演論文集 第61回理論応用力学講演会

巻号頁・発行日

pp.88, 2012 (Released:2012-03-28)

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本発表では,丸め誤差のない新たな数値微分近似手法として複素数階微分法を提示する.本手法を大変形材料構成則の応力および整合接線剛性の導出に応用した事例を紹介する.ここでは,陰的解法の代表的な汎用FEMソフトウェアであるAbaqus/Standardの材料構成則のユーザサブルーチンUMATを例にとり,その実装方法について示す.また,いくつかの数値計算例を通して,本手法の有効性を示す.

著者

藤川 正毅 田中 真人 井元 佑介 三目 直登 浦本 武雄 山中 脩也

出版者

一般社団法人 日本機械学会

雑誌

日本機械学会論文集

巻号頁・発行日

vol.86, no.881, pp.19-00256-19-00256, 2020

被引用文献数

1

---

<p>A numerical calculation scheme for stress and its consistent tangent moduli with hyper-dual numbers(HDN) for Ogden-type hyperelastic material model was proposed. The main advantage of this scheme is that once the framework is coded, any Ogden-type hyperelastic material model can be implemented by only re-coding the strain energy density function. In this scheme, the new differentiation method for eigenvalue and eigenvector of the symmetric matrices with HDN were proposed. The proposed method can calculate the eigenvalue and eigenvector in non-real part analytically by using the eigenvalue and eigenvector in real part, in case that all eigenvalues in real part are not multiple root. We implemented the Neo-Hookean model and the Ogden model with the proposed scheme, to confirm the effectiveness and robustness of this method, and applied it to some examples. As the results, it was confirmed that the numerical results of the proposed method showed good agreement with analytical ones.</p>

著者

藤川 正毅 田中 真人 井元 佑介 三目 直登 浦本 武雄 山中 脩也

出版者

一般社団法人 日本機械学会

雑誌

日本機械学会論文集

巻号頁・発行日

2019

被引用文献数

1

---

<p>A numerical calculation scheme for stress and its consistent tangent moduli with hyper-dual numbers(HDN) for Ogden-type hyperelastic material model was proposed. The main advantage of this scheme is that once the framework is coded, any Ogden-type hyperelastic material model can be implemented by only re-coding the strain energy density function. In this scheme, the new differentiation method for eigenvalue and eigenvector of the symmetric matrices with HDN were proposed. The proposed method can calculate the eigenvalue and eigenvector in non-real part analytically by using the eigenvalue and eigenvector in real part, in case that all eigenvalues in real part are not multiple root. We implemented the Neo-Hookean model and the Ogden model with the proposed scheme, to confirm the effectiveness and robustness of this method, and applied it to some examples. As the results, it was confirmed that the numerical results of the proposed method showed good agreement with analytical ones.</p>

著者

藤川 正毅 山辺 純一郎 小石 正隆

出版者

一般社団法人 日本機械学会

雑誌

計算力学講演会講演論文集

巻号頁・発行日

vol.2017, 2017

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Industrial rubber, commonly used in the fabrication of tires and engine mounts, exhibits nonlinear viscoelastic behavior. In the design of these rubber products, it is important to capture the stress–strain responses under arbitrary loading conditions. However, the stress–strain responses exhibit complicated behavior, which depends on strain rate, strain history, strain amplitude, etc. The main purpose of this study is to develop a new constitutive model that captures the nonlinear viscoelastic stress–strain response of carbon-black-filled styrene-butadiene rubber vulcanizates (SBR-CB). In the assumed micro-mechanical network structure, we decomposed the isochoric free energy into the elastic equilibrium and the viscoelastic overstress response. Based on the results of our performance evaluation of various hyperplastic material models, we used an eight-chain model for the equilibrium network. For the nonlinear viscoelastic network, we used the micro-sphere model. The micro-stress/strain equation was assumed to be in simple phenomenological form, as reported by Miehe. For the revolution equation of the micro-inelastic strain, the Rendek and Lion model was employed. In addition, to reproduce the stress-strain relationship under from infinitesimal to 50% strain amplitude, the relaxation time depending on the strain amplitude of the free dangling chains was proposed as a new metric. The proposed model was able to practically and precisely reproduce the dynamic responses of SBR-CB25 under a wide range of applied strains and strain rates, was thermodynamically consistent for arbitrary deformation, could be implemented in commercial FEM software (Abaqus), and reproduced the stress-strain relationship under various experimental loading conditions.

著者

田中 興 藤川 正毅 真壁 朝敏 石川 清貴

出版者

一般社団法人 日本機械学会

雑誌

計算力学講演会講演論文集 2015.28 (ISSN:24242799)

巻号頁・発行日

pp._223-1_-_223-2_, 2015-10-10 (Released:2017-06-19)

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ゲル材料は高い衝撃吸収性能などの特異な性質をもつものが多く開発されている.そしてゲル材料の性能を評価するためのシミュレーション法の確立が望まれている.その中でも特に長期使用環境下におけるゲル材料の力学特性の研究は,重要性があるにも関わらず研究が進んでいないのが現状である.そこで本研究では商用ゲル材料を対象とし,大変形下におけるクリープ挙動を実験により明らかにする.そして,シミュレーションのための材料モデルとその材料定数値について検討し,その有効性を確認する.

著者

藤川 正毅 石川 清貴 真壁 朝敏 田中 真人 笹川 崇 表 竜二

出版者

一般社団法人 日本機械学会

雑誌

日本機械学会論文集 (ISSN:21879761)

巻号頁・発行日

2016

被引用文献数

2

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This paper presents a novel Formulated Alpha FEM with deviatoric / volumetric split, which is combination of standard FEM and Node-based Smoothed FEM (NS-FEM), to compute highly accurate deformation in mechanical problems using tetrahedral elements. The essential idea of the method is the use of a deviatoric alpha formulated on basis of the results of cantilever problem, and the volumetric alpha introduced NS-FEM. The features of this proposed method are: 1) immune from volumetric locking, 2) less sensitive to element distortion, and 3) to be carried out with the same preprocessing as standard FEM from user's viewpoint. Several numerical examples show that the present method achieves higher accuracy compared to the standard FEM and Edge-based/NS-FEM which is known to be one of the best S-FEM formulations.

著者

中山 卓弥 真壁 朝敏 藤川 正毅 新川 和夫

出版者

一般社団法人 日本高圧力技術協会

雑誌

圧力技術 (ISSN:03870154)

巻号頁・発行日

vol.54, no.2, pp.50-59, 2016

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The fatigue limit and crack growth behavior of slit specimens of epoxy base carbon composites were investigated. The fatigue limit was defined by maximum stress amplitude that the specimen endured 106 times stress repeating. Also, that was calculated by net stress at ligament. Carbon fiber directions were parallel and perpendicular to the load axis. The highest value of fatigue limit was obtained when all fiber directions were parallel to the load axis. However, crack grew along the fiber direction or load axis in the case of long slit. In the cases of two carbon directions that is, parallel and perpendicular to the load axis, the fatigue limits were evaluated from the result of the specimen that all carbon directions were parallel to the load axis. When measured value of fatigue limit was higher than the evaluated value, it was expected that the strain constraint occurred due to resistance of fiber in perpendicular to the load axis. When the measured value was lower, the peeling of fiber from epoxy was expected to be occurred. According to those results, it was expected that fatigue limit of smooth specimen of carbon composites with long fiber can be evaluated from the results of slit specimens

著者

中山 卓弥 真壁 朝敏 藤川 正毅 新川 和夫

出版者

一般社団法人 日本高圧力技術協会

雑誌

圧力技術 (ISSN:03870154)

巻号頁・発行日

vol.54, no.2, pp.50-59, 2016-03-25 (Released:2016-04-29)

参考文献数

7

---

The fatigue limit and crack growth behavior of slit specimens of epoxy base carbon composites were investigated. The fatigue limit was defined by maximum stress amplitude that the specimen endured 106 times stress repeating. Also, that was calculated by net stress at ligament. Carbon fiber directions were parallel and perpendicular to the load axis. The highest value of fatigue limit was obtained when all fiber directions were parallel to the load axis. However, crack grew along the fiber direction or load axis in the case of long slit. In the cases of two carbon directions that is, parallel and perpendicular to the load axis, the fatigue limits were evaluated from the result of the specimen that all carbon directions were parallel to the load axis. When measured value of fatigue limit was higher than the evaluated value, it was expected that the strain constraint occurred due to resistance of fiber in perpendicular to the load axis. When the measured value was lower, the peeling of fiber from epoxy was expected to be occurred. According to those results, it was expected that fatigue limit of smooth specimen of carbon composites with long fiber can be evaluated from the results of slit specimens

著者

藤川 正毅 石川 清貴 真壁 朝敏 田中 真人 笹川 崇 表 竜二

出版者

一般社団法人 日本機械学会

雑誌

日本機械学会論文集 (ISSN:21879761)

巻号頁・発行日

vol.82, no.834, pp.15-00454-15-00454, 2016

被引用文献数

5

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This paper proposes a novel implementation scheme of geometrically nonlinear finite element programs, which automatically compute exact internal force vectors and element stiffness matrices by numerically differentiating a strain energy function at each element. This method can significantly simplify the complex implementation procedure which is often observed in conventional finite element implementations, since it never requires B matrices, stress tensors, and elastic tensors by hand. The proposed method is based on a highly accurate numerical derivatives which use hyper-dual numbers and never suffer from any round-off and truncation errors. Several numerical examples are performed to demonstrate the effectiveness and robustness of the proposed method.

著者

藤川 正毅 石川 清貴 真壁 朝敏 田中 真人 笹川 崇 表 竜二

出版者

The Japan Society of Mechanical Engineers

雑誌

日本機械学会論文集 (ISSN:21879761)

巻号頁・発行日

2016

被引用文献数

5

---

This paper proposes a novel implementation scheme of geometrically nonlinear finite element programs, which automatically compute exact internal force vectors and element stiffness matrices by numerically differentiating a strain energy function at each element. This method can significantly simplify the complex implementation procedure which is often observed in conventional finite element implementations, since it never requires B matrices, stress tensors, and elastic tensors by hand. The proposed method is based on a highly accurate numerical derivatives which use hyper-dual numbers and never suffer from any round-off and truncation errors. Several numerical examples are performed to demonstrate the effectiveness and robustness of the proposed method.

著者

藤川 正毅 三上 貴央 小林 卓哉 隆 雅久

出版者

日本実験力学会

雑誌

実験力学 (ISSN:13464930)

巻号頁・発行日

vol.7, no.4, pp.387-392, 2007 (Released:2008-06-25)

参考文献数

12

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The authors have developed a new automatic technique of drawing the master curve from the experimental data measured by the Dynamic Measurement Tester. In this paper, the experimental conditions recommended by Japanese Industrial Standards are considered and modified from the perspective of drawing the master curve. To verify the effectiveness of the proposed technique and the experimental conditions, the storage and loss moduli of epoxy resins and rubber materials are measured, and the proposed technique is applied to the experimental data. From the results, it is confirmed that the master curves are obtained automatically and expeditiously.